%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWX207+1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 09:15:17 AM UTC 2026
% Result : Theorem 3.94s 2.86s
% Output : Refutation 4.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 27
% Syntax : Number of formulae : 56 ( 53 unt; 0 typ; 0 def)
% Number of atoms : 59 ( 58 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 182 ( 29 ~; 0 |; 0 &; 150 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 19 usr; 7 con; 0-2 aty)
% Number of variables : 62 ( 0 ^; 56 !; 6 ?; 62 :)
% Comments :
%------------------------------------------------------------------------------
thf(linC_decl,type,
linC: $i > $i ).
thf(bP_decl,type,
bP: $i > $i ).
thf(pA_decl,type,
pA: $i ).
thf(aP_decl,type,
aP: $i > $i ).
thf(pB_decl,type,
pB: $i ).
thf(pE_decl,type,
pE: $i ).
thf(linP_decl,type,
linP: $i > $i ).
thf(cons_decl,type,
cons: $i > $i > $i ).
thf(b_decl,type,
b: $i ).
thf(nil_decl,type,
nil: $i ).
thf(a_decl,type,
a: $i ).
thf(head_decl,type,
head: $i > $i ).
thf(proj1AP_decl,type,
proj1AP: $i > $i ).
thf(proj1BP_decl,type,
proj1BP: $i > $i ).
thf(tail_decl,type,
tail: $i > $i ).
thf(append_decl,type,
append: $i > $i > $i ).
thf(proj2C_decl,type,
proj2C: $i > $i ).
thf(c2_decl,type,
c2: $i > $i > $i ).
thf(proj1C_decl,type,
proj1C: $i > $i ).
thf(28,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ c2 ) @ linC )
= ( B @ linP @ ( A @ linP @ append ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_026) ).
thf(115,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ c2 ) @ linC )
= ( B @ linP @ ( A @ linP @ append ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(9,axiom,
! [A: $i] :
( ( A @ aP )
!= pB ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_009) ).
thf(56,plain,
! [A: $i] :
( ( A @ aP )
!= pB ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(8,axiom,
! [A: $i] :
( ( A @ bP )
!= pB ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_012) ).
thf(52,plain,
! [A: $i] :
( ( A @ bP )
!= pB ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(26,axiom,
! [A: $i] :
( ( A @ bP @ linP )
= ( nil @ ( b @ cons ) @ ( A @ linP @ append ) @ ( nil @ ( b @ cons ) @ append ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_022) ).
thf(109,plain,
! [A: $i] :
( ( A @ bP @ linP )
= ( nil @ ( b @ cons ) @ ( A @ linP @ append ) @ ( nil @ ( b @ cons ) @ append ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ cons ) @ head )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_001) ).
thf(64,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ cons ) @ head )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ( A @ aP )
!= ( B @ bP ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_007) ).
thf(91,plain,
! [A: $i,B: $i] :
( ( A @ aP )
!= ( B @ bP ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(3,axiom,
! [A: $i] :
( ( A @ bP )
!= pA ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_011) ).
thf(35,plain,
! [A: $i] :
( ( A @ bP )
!= pA ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(27,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ c2 ) @ proj1C )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_017) ).
thf(112,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ c2 ) @ proj1C )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(21,axiom,
! [A: $i] :
( ( A @ aP @ linP )
= ( nil @ ( a @ cons ) @ ( A @ linP @ append ) @ ( nil @ ( a @ cons ) @ append ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_021) ).
thf(95,plain,
! [A: $i] :
( ( A @ aP @ linP )
= ( nil @ ( a @ cons ) @ ( A @ linP @ append ) @ ( nil @ ( a @ cons ) @ append ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( nil
!= ( B @ ( A @ cons ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_003) ).
thf(67,plain,
! [A: $i,B: $i] :
( nil
!= ( B @ ( A @ cons ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(5,axiom,
pB != pE,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_016) ).
thf(43,plain,
pB != pE,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(24,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( B @ cons ) @ append ) )
= ( A @ ( C @ append ) @ ( B @ cons ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_020) ).
thf(104,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( B @ cons ) @ append ) )
= ( A @ ( C @ append ) @ ( B @ cons ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(15,axiom,
! [A: $i] :
( ( A @ aP @ proj1AP )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_005) ).
thf(75,plain,
! [A: $i] :
( ( A @ aP @ proj1AP )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(25,axiom,
( ( pE @ linP )
= nil ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_025) ).
thf(107,plain,
( ( pE @ linP )
= nil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(11,axiom,
( ( pA @ linP )
= ( nil @ ( a @ cons ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_023) ).
thf(62,plain,
( ( pA @ linP )
= ( nil @ ( a @ cons ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(23,axiom,
! [A: $i] :
( ( A @ ( nil @ append ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_019) ).
thf(101,plain,
! [A: $i] :
( ( A @ ( nil @ append ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(19,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ cons ) @ tail )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_002) ).
thf(88,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ cons ) @ tail )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(6,axiom,
pA != pB,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_014) ).
thf(46,plain,
pA != pB,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(16,axiom,
! [A: $i] :
( ( A @ bP @ proj1BP )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_006) ).
thf(78,plain,
! [A: $i] :
( ( A @ bP @ proj1BP )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(1,conjecture,
? [A: $i,B: $i] :
~ ( ( ( A @ linC )
= ( B @ linC ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal_027) ).
thf(2,negated_conjecture,
~ ? [A: $i,B: $i] :
~ ( ( ( A @ linC )
= ( B @ linC ) )
=> ( A = B ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(29,plain,
~ ? [A: $i,B: $i] :
~ ( ( ( A @ linC )
= ( B @ linC ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(10,axiom,
( ( pB @ linP )
= ( nil @ ( b @ cons ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_024) ).
thf(60,plain,
( ( pB @ linP )
= ( nil @ ( b @ cons ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(18,axiom,
a != b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_004) ).
thf(85,plain,
a != b,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(14,axiom,
! [A: $i] :
( ( A @ aP )
!= pE ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_010) ).
thf(71,plain,
! [A: $i] :
( ( A @ aP )
!= pE ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(7,axiom,
pA != pE,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_015) ).
thf(49,plain,
pA != pE,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(17,axiom,
! [A: $i] :
( ( A @ bP )
!= pE ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_013) ).
thf(81,plain,
! [A: $i] :
( ( A @ bP )
!= pE ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(4,axiom,
! [A: $i] :
( ( A @ aP )
!= pA ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_008) ).
thf(39,plain,
! [A: $i] :
( ( A @ aP )
!= pA ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(22,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ c2 ) @ proj2C )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_018) ).
thf(98,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ c2 ) @ proj2C )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(118,plain,
$false,
inference(e,[status(thm)],[115,56,52,109,64,91,35,112,95,67,43,104,75,107,62,101,88,46,78,29,60,85,71,49,81,39,98]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX207+1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.13/0.40 % Computer : n010.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Sat Sep 26 16:56:15 UTC 2026
% 0.13/0.41 % CPUTime :
% 0.13/0.41 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 1.02/1.05 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.24/1.29 % [INFO] Parsing done (245ms).
% 1.39/1.31 % [INFO] Running in sequential loop mode.
% 2.08/1.84 % [INFO] eprover registered as external prover.
% 2.08/1.85 % [INFO] Scanning for conjecture ...
% 2.23/1.98 % [INFO] Found a conjecture (or negated_conjecture) and 26 axioms. Running axiom selection ...
% 2.40/2.08 % [INFO] Axiom selection finished. Selected 26 axioms (removed 0 axioms).
% 2.40/2.13 % [INFO] Problem is first-order (TPTP FOF).
% 2.40/2.14 % [INFO] Type checking passed.
% 2.56/2.15 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 3.94/2.86 % External prover 'e' found a proof!
% 3.94/2.86 % [INFO] Killing All external provers ...
% 3.94/2.86 % Time passed: 2311ms (effective reasoning time: 1534ms)
% 3.94/2.86 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 3.94/2.86 % Axioms used in derivation (26): axiom_024, axiom_010, axiom_021, axiom_002, axiom_023, axiom_016, axiom_005, axiom_012, axiom_001, axiom_022, axiom_011, axiom_025, axiom_003, axiom_014, axiom_007, axiom_018, axiom_009, axiom_017, axiom_013, axiom_006, axiom_015, axiom_004, axiom_026, axiom_020, axiom_019, axiom_008
% 3.94/2.86 % No. of inferences in proof: 56
% 3.94/2.86 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2311 ms resp. 1534 ms w/o parsing
% 4.30/2.93 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.30/2.93 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------